Improved proof-by-contraction method and relative homologous entropy inequalities
Abstract The celebrated holographic entanglement entropy triggered investigations on the connections between quantum information theory and quantum gravity. An important achievement is that we have gained more insights into the quantum states. It allows us to diagnose whether a given quantum state i...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-06-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP06(2022)153 |
| _version_ | 1797865763826040832 |
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| author | Nan Li Chuan-Shi Dong Dong-Hui Du Fu-Wen Shu |
| author_facet | Nan Li Chuan-Shi Dong Dong-Hui Du Fu-Wen Shu |
| author_sort | Nan Li |
| collection | DOAJ |
| description | Abstract The celebrated holographic entanglement entropy triggered investigations on the connections between quantum information theory and quantum gravity. An important achievement is that we have gained more insights into the quantum states. It allows us to diagnose whether a given quantum state is a holographic state, a state whose bulk dual admits semiclassical geometrical description. The effective tool of this kind of diagnosis is holographic entropy cone (HEC), an entropy space bounded by holographic entropy inequalities allowed by the theory. To fix the HEC and to prove a given holographic entropy inequality, a proof-by-contraction technique has been developed. This method heavily depends on a contraction map f, which is very difficult to construct especially for more-region (n ≥ 4) cases. In this work, we develop a general and effective rule to rule out most of the cases such that f can be obtained in a relatively simple way. In addition, we extend the whole framework to relative homologous entropy, a generalization of holographic entanglement entropy that is suitable for characterizing the entanglement of mixed states. |
| first_indexed | 2024-04-09T23:14:28Z |
| format | Article |
| id | doaj.art-be35f222900a47499fd060b4e74de3da |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T23:14:28Z |
| publishDate | 2022-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-be35f222900a47499fd060b4e74de3da2023-03-22T10:12:10ZengSpringerOpenJournal of High Energy Physics1029-84792022-06-012022612810.1007/JHEP06(2022)153Improved proof-by-contraction method and relative homologous entropy inequalitiesNan Li0Chuan-Shi Dong1Dong-Hui Du2Fu-Wen Shu3Department of Physics, Nanchang UniversityDepartment of Physics, Nanchang UniversitySchool of Physics and Astronomy, Sun Yat-sen UniversityDepartment of Physics, Nanchang UniversityAbstract The celebrated holographic entanglement entropy triggered investigations on the connections between quantum information theory and quantum gravity. An important achievement is that we have gained more insights into the quantum states. It allows us to diagnose whether a given quantum state is a holographic state, a state whose bulk dual admits semiclassical geometrical description. The effective tool of this kind of diagnosis is holographic entropy cone (HEC), an entropy space bounded by holographic entropy inequalities allowed by the theory. To fix the HEC and to prove a given holographic entropy inequality, a proof-by-contraction technique has been developed. This method heavily depends on a contraction map f, which is very difficult to construct especially for more-region (n ≥ 4) cases. In this work, we develop a general and effective rule to rule out most of the cases such that f can be obtained in a relatively simple way. In addition, we extend the whole framework to relative homologous entropy, a generalization of holographic entanglement entropy that is suitable for characterizing the entanglement of mixed states.https://doi.org/10.1007/JHEP06(2022)153AdS-CFT CorrespondenceGauge-Gravity CorrespondenceHolography and Condensed Matter Physics (AdS/CMT) |
| spellingShingle | Nan Li Chuan-Shi Dong Dong-Hui Du Fu-Wen Shu Improved proof-by-contraction method and relative homologous entropy inequalities Journal of High Energy Physics AdS-CFT Correspondence Gauge-Gravity Correspondence Holography and Condensed Matter Physics (AdS/CMT) |
| title | Improved proof-by-contraction method and relative homologous entropy inequalities |
| title_full | Improved proof-by-contraction method and relative homologous entropy inequalities |
| title_fullStr | Improved proof-by-contraction method and relative homologous entropy inequalities |
| title_full_unstemmed | Improved proof-by-contraction method and relative homologous entropy inequalities |
| title_short | Improved proof-by-contraction method and relative homologous entropy inequalities |
| title_sort | improved proof by contraction method and relative homologous entropy inequalities |
| topic | AdS-CFT Correspondence Gauge-Gravity Correspondence Holography and Condensed Matter Physics (AdS/CMT) |
| url | https://doi.org/10.1007/JHEP06(2022)153 |
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